Recently there has been a new theoretical direction in harnessing the richness of nonlinear dynamics, namely the exploitation of chaos to do flexible computations. This so-called chaos computing paradigm is driven by the motivation to use new concepts of physics to build better computing devices. The chaos computing paradigm is further discussed in S. Sinha, W. L. Ditto, Phys Rev Lett. 81 (1998) 2156; Phys. Rev. E 60 (1999) 363; S. Sinha, T. Munakata, W. L. Ditto, Phys Rev E 65 (2002) 036216; K. Murali, S. Sinha, W. L. Ditto, Int. J. of Bifur. Chaos Appl. Sci. Eng. 13 (2003) 2669; Phys Rev E 68 (2003) 016205; K. Murali, S. Sinha, I. Raja Mohamed, Phys. Lett. A 339 (2005) 39; K. E. Chlouverakis, M. J. Adams, Electronics Lett. 41 (2005) 359; D. Cafagna, G. Grassi, Int. Sym. Signals, Circuits and Systems (ISSCS 2005) 2 (2005) 749; M. R. Jahed-Motlagh, B. Kia, W. L. Ditto, S. Sinha, Int. J. of Bifur. Chaos Appl. Sci. Eng. 17 (2007) 1955; K. Murali, S. Sinha, Phys Rev E 75 (2007) 025201(R); and B. Prusha, J. Lindner, Phys. Lett. A 263 (1999) 105, which are hereby incorporated by reference in their entireties.
The general strategy underlying this research activity exploits the determinism of dynamics on one hand, and its richness on the other. The determinism allows one to reverse engineer, so to speak, and the richness of dynamical patterns allows flexibility and versatility in accomplishing wide-ranging operations. This novel paradigm forms part of the over-arching attempt to find new ways to exploit physical phenomena that are well understood in the context of physics, to do computations, and in particular to bridge dynamical phenomena and computations (See, for example, J. P. Crutchfield, K. Young, Phys. Rev. Lett. 63 (1989) 105; J. P. Crutchfield, Physica D 75 (1994) 11; N. Margolus, Physica D 10 (1984) 81; T. Toffoli, N. Margolus, “Cellular Automata Machines: A New Environment for Modelling”, MIT Press (1987); T. Toffoli, N. Margolus, Physica D 47 (1990) 263; C. Moore, Phys. Rev. Lett. 64 (1990) 2354; A. V. Holden, J. V. Tucker, H. Zhang, M. J. Poole, Chaos 2 (1992) 367; A. Toth, K. J. Showalter, J. Chem. Phys. 103 (1995) 2058; M. M. Mano, “Computer System Architecture”, 3rd Ed. Prentice Hall, Englewood Cliffs, N.J. (1993); and T. C. Bartee, “Computer Architecture and Logic Design”, McGraw-Hill, New York, (1991), which are hereby incorporated by reference in their entireties).
The fundamental components of computer architecture today are the logical AND, OR, NOT, and XOR operations, from which we can directly obtain basic operations like bit-by-bit addition and memory (See, for example, T. C. Bartee, “Computer Architecture and Logic Design”, McGraw-Hill, New York, (1991)). A typical 2-input operation act on two inputs I1 and I2 and outputs a signal O. The type of logic is defined by patterns of input-to-output mapping represented by the truth table in Table I. Now all the above mentioned gates can be constructed by combining the NOR or NAND operations (See, for example, T. C. Bartee, “Computer Architecture and Logic Design”, McGraw-Hill, New York, (1991)). Clearly though, this conversion process is inefficient in comparison with direct implementation, considering perhaps that such fundamental operations may be performed a large number of times.